64-18=96(-m2+1)

Solution for 64-18=96(-m2+1) equation:

64-18=96(-m2+1)

We move all terms to the left:

64-18-(96(-m2+1))=0

We add all the numbers together, and all the variables

-(96(-1m^2+1))+64-18=0

We add all the numbers together, and all the variables

-(96(-1m^2+1))+46=0


We calculate terms in parentheses: -(96(-1m^2+1)), so:

96(-1m^2+1)

We multiply parentheses

-96m^2+96

Back to the equation:

-(-96m^2+96)


We get rid of parentheses

96m^2-96+46=0

We add all the numbers together, and all the variables

96m^2-50=0

a = 96; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·96·(-50)
Δ = 19200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{3}}{2*96}=\frac{0-80\sqrt{3}}{192}
=-\frac{80\sqrt{3}}{192}
=-\frac{5\sqrt{3}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{3}}{2*96}=\frac{0+80\sqrt{3}}{192}
=\frac{80\sqrt{3}}{192}
=\frac{5\sqrt{3}}{12}
$